Comparing Dual with Single Treatments in Block Designs
研究在必须排除特定治疗组合的区组实验中，如何比较双重治疗与单一治疗的效果，推导了对比估计量平均方差的下界，并构造了高效的强化群可分割设计。
Experiments having two treatment factors and one blocking factor are considered in which a particular combination of treatment factor levels must be excluded. The motivation for the work is a medical trial of two drugs in which a double placebo cannot be administered on ethical grounds. The contrasts of interest compare the effects of having both treatment factors at nonzero labelled levels with the effects of having only one treatment factor at a nonzero labelled level. A lower bound is derived on the average variance of the contrast estimators in n×m experiments. For n × 2 experiments a balance property is defined which is possessed by many efficient designs. Designs having the property are characterized through the structure of the intra-block information matrix. Efficient reinforced group divisible designs are constructed and assessed against the lower bound.